Question

Если лодка движется по течению реки,то за 2 часа она проходит 10км.А если она движется против течения ,то за тоже время она проходит только 6 км .Найди скорость лодки и скорость течения реки.

Answer 1

Ответ:

4 км/ч, 1 км/ч

Объяснение:

10 км/2ч=5км/ч

6 км/2 ч=3 км/ч

Дано:

V1= 5 км/ч

V2= 3 км/ч

Vp.-?

Vл.-?

Решение:

пусть скорость реки-х

тогда, 5-х=3+х

-2х=-2

х=1 (км/ч)

отсюда,

Vл.=5-1=4(км/ч)

=3+1=4(км/ч)

Answer 2

Finding the Speed of the Boat and the Speed of the River Current

To find the speed of the boat and the speed of the river current, we can set up a system of equations based on the given information.

Let's assume the speed of the boat is represented by b and the speed of the river current is represented by c.

When the boat is moving downstream (with the current), its effective speed is the sum of the boat's speed and the current's speed. Therefore, the boat's effective speed is b + c.

According to the given information, when the boat is moving downstream, it covers a distance of 10 km in 2 hours. This can be represented by the equation:

2(b + c) = 10 When the boat is moving upstream (against the current), its effective speed is the difference between the boat's speed and the current's speed. Therefore, the boat's effective speed is b - c.

According to the given information, when the boat is moving upstream, it covers a distance of 6 km in 2 hours. This can be represented by the equation:

2(b - c) = 6 Now we have a system of two equations with two unknowns (b and c). We can solve this system of equations to find the values of b and c.

Solving the System of Equations

To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of substitution.

From equation we can express b in terms of c:

b = 5 - c (dividing both sides of equation by 2)

Now we substitute this expression for b in equation:

2((5 - c) - c) = 6

Simplifying the equation:

2(5 - 2c) = 6

Expanding and simplifying further:

10 - 4c = 6

Rearranging the equation:

4c = 10 - 6

4c = 4

Dividing both sides by 4:

c = 1

Now that we have the value of c, we can substitute it back into the expression for b:

b = 5 - c

b = 5 - 1

b = 4

Therefore, the speed of the boat is 4 km/h and the speed of the river current is 1 km/h.

Conclusion

The speed of the boat is 4 km/h and the speed of the river current is 1 km/h.